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arXiv · 2603.12774

Synchronization by noise for stochastic differential equations driven by fractional Brownian motion

Alexandra Blessing·Mazyar Ghani Varzaneh
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Abstract

We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index $H\in(0,1)$. Provided that the SDE has a negative top Lyapunov exponent, we show that a weak form of synchronization occurs. To this aim we use tools from stochastic dynamical systems, random dynamical systems and characterize the support of an invariant measure of a random dynamical system in a non-Markovian setting.

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Alexandra Blessing, Mazyar Ghani Varzaneh. 2026-03-13. Synchronization by noise for stochastic differential equations driven by fractional Brownian motion. https://arxiv.org/abs/2603.12774

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